|
%I #17 Dec 04 2021 08:16:23
%S 0,1,5,18,60,203,725,2772,11368,49853,232757,1151902,6018772,33087191,
%T 190780197,1150653904,7241710912,47454745785,323154696165,
%U 2282779990474,16700904488684,126356632390275,987303454928949
%N a(n) = Sum_{i = 1..n} (n - i)^(1 + i).
%H Seiichi Manyama, <a href="/A062809/b062809.txt">Table of n, a(n) for n = 1..600</a>
%F a(n) ~ sqrt(2*Pi) * ((n + 1)/LambertW(exp(1)*(n + 1)))^(1/2 + (n + 1)*(1 - 1/LambertW(exp(1)*(n + 1)))) / sqrt(1 + LambertW(exp(1)*(n + 1))). - _Vaclav Kotesovec_, Dec 04 2021
%p a:=n->sum((n-j)^j,j=2..n): seq(a(n), n=2..24); # _Zerinvary Lajos_, Jun 07 2008
%t Sum[(n - i)^(1 + i), {i, 1, n}]
%o (PARI) a(n) = sum(i=1, n, (n-i)^(1+i)); \\ _Michel Marcus_, Mar 24 2019
%Y Cf. A003101, A349878, A349879.
%K nonn,easy
%O 1,3
%A _Olivier Gérard_, Jun 23 2001
|
